These are all the known approximation algorithms for the diameter problem in arbitrary graphs: the scheme of [1]}, [2]} for undirected graphs, and the three algorithms for directed graphs: the exact \(\tilde{O}(mn)\)  time algorithm using APSP, the \(\tilde{O}(m)\)  time 2-approximation and the \(3/2\) -approximation algorithms of [2]}, [4]}.
In Figure REF  the known algorithms are represented as purple and pink points.
